Variables to Represent Two Quantities

Variables on Both Sides

Unit 1 Lesson 1.4

Overview of The Agenda

• Part 1: Warm-Up Review

• Part 2: Introduction to Variables on Both Sides

• Part 3: Independent Practice Problems

Poll

Attendance Checker: Would you prefer a Ford or a Chevy? (You have 45 seconds.)

Open Ended

Part 1 Warm-up: You have 3 minutes to complete the following problems. (This will count as a participation grade.)

Solve for x.

$$1.\ -5\left(x-2\right)+2x=40$$

$$2.\ -\left(2x+4\right)=12$$    

Solutions to the warm-up problems.

Part 2: Introduction to Variables on Both Sides

Unit 1 Section 1.5 Variables on Both Sides of The Equal Sign

At the end of this lesson, students will be able to..

• solve equations with variables on both sides.

Variables on Both Sides of The Equal Sign

The goal is to get all the variables on the same side. You can add or subtract terms with variables in them, just like you add or subtract numbers on each side.

The goal is to move the variable term from the right side of the equal sign to the left side of the equal sign.

Multiple Choice

Then, it becomes a simple two-step equation. Solve the equation for x.

$$2x+1=5$$  

• 3

• 2

• 5

• 9

Poll

Example 2

$$-2x+12=3x-8$$  

Which variable term do you think we should move first? (Hint: We want it to look similar to a two-step equation.)

• -2x

• 3x

Both are right!

You have a choice to either try to cancel out the variable term on the left or cancel the variable term on the right. Either choice is fine, you'll get the same answer either way.

Open Ended

Example 3

Solve the following problem for t.

$$16-2t=5t+9$$  

Check yourself.

Open Ended

Example 4

Solve the following problem for g.

$$7g+2=-3g+302$$  

Check yourself.

Poll

Temperature Check - How do you feel?

• Thumbs Up - I am great and can teach this lesson to someone.

• Thumbs In The Middle - I think I understand, and may need a little guidance.

• Thumbs Down - I have no idea what you’re talking about Ms. Wilkinson.

Example 5

• Step 1: Distributive property

• Step 2: Move variables to one side of the equal sign.

• Step 3: Solve the two-step equation.

Open Ended

Example 6

Solve the following equation


$$5\left(x+2\right)=3x-8$$  

Check yourself.

Multiple Choice

Example 7

Solve the following problem for x.

$$-3x-32=-2\left(5-4x\right)$$  

• 2

• -4.2

• -2

• 22

Check yourself.

Poll

Temperature Check - How do you feel?

• Thumbs Up - I am great and can teach this lesson to someone.

• Thumbs In The Middle - I think I understand, and may need a little guidance.

• Thumbs Down - I have no idea what you’re talking about Ms. Wilkinson.

Independent Classwork

• 15 problems

• With and without distributive property

• 40 minutes (or the remainder of class)

• Joinmyquiz.com and use the code: 15212272

• Use your first and last name.

• If at anytime you need help, ask Ms. Wilkinson for a breakout room session.